Tight bound on treedepth in terms of pathwidth and longest path

Abstract

We show that every graph with pathwidth strictly less than $a$ that contains no path on $2^b$ vertices as a subgraph has treedepth at most $10ab$. The bound is best possible up to a constant factor.

arXiv commentv3: corrected some typos. v2: revised following referees' comments, corrects an error in v1

References in corpus (1)

• Approximating pathwidth for graphs of small treewidth